A frictionless contact problem for a flexible circular plate and an incompressible non-homogeneous elastic halfspace

• The halfspace is considered to be non-homogeneous where the shear modulus varies exponentially with depth.
• The effect of relative rigidity of the plate has been analyzed on the response.
• Accuracy of the solution has been checked with existing limiting solutions and FEM analysis.
• The results are used to test the accuracy of a computational scheme.

In this paper we apply an energy method to examine the axisymmetric contact problem for a flexible circular plate in smooth contact an incompressible elastic halfspace, where the linear elastic shear modulus varies exponentially with depth. The approach adopted approximates the deflected shape of the plate by a power series expansion which satisfies the kinematics of deformation of the plate and the Kirchhoff boundary condition at the edge of the plate. The coefficients in the series are evaluated by making use of the principle of minimum potential energy. Results are obtained for the maximum deflection, the relative deflection and the maximum flexural moment in the circular plate. The results derived from the proposed procedure are compared with equivalent results derived from a computational procedure.